AbstractAn elementary proof is given of the theorem: If D = −3q or −27q is the discriminant of a cubic field, where q ≡ 1 (mod 4) is a prime, and if p or 4p is represented by c2 + ∥ D ∥ d2, then the fundamental unit in the field Q(q12) is a cubic residue of the prime p. In special cases necessary and sufficient conditions are derived
AbstractCriteria are obtained for the quartic residue character of the fundamental unit of the real ...
There exists a positive density of fundamental discriminants D such that the attached fundamental un...
AbstractNecessary and sufficient conditions for representing certain classes of primes by given quad...
AbstractAn elementary proof is given of the theorem: If D = −3q or −27q is the discriminant of a cub...
AbstractLet p≡1(mod4) be a prime. Let a,b∈Z with p∤a(a2+b2). In the paper we mainly determine (b+a2+...
Criteria are obtained for the quartic residue character of the fundamental unit of the real quadrati...
Let εmdenote the fundamental unit of the real quadratic field Q(Vm). It is our purpose to evaluate t...
AbstractLet K be the cubic subfield of a field of the 163rd root of unity. It is proved that the cla...
AbstractLet K be the cubic subfield of a field of the 163rd root of unity. It is proved that the cla...
Let f(x) = x3 − tx2−ux−1 ∈ Z[x]. Conditions are given on t and u which ensure that f(x) has exactly...
AbstractLet p>3 be a prime, u,v,d∈Z, gcd(u,v)=1, p∤u2−dv2 and (−3dp)=1, where (ap) is the Legendre s...
AbstractLet ∈ = (t + u(d)2/2 be a unit of Q((d)1/2), whose norm = 1. We investigate the properties o...
AbstractLet ϵ be an algebraic unit such that rank of the unit group of the order Z[ϵ] is equal to on...
Dirichlet's theorem describes the structure of the group of units of the ring of algebraic integers ...
AbstractExplicit formulas are given for the quadratic and quartic characters of units of certain qua...
AbstractCriteria are obtained for the quartic residue character of the fundamental unit of the real ...
There exists a positive density of fundamental discriminants D such that the attached fundamental un...
AbstractNecessary and sufficient conditions for representing certain classes of primes by given quad...
AbstractAn elementary proof is given of the theorem: If D = −3q or −27q is the discriminant of a cub...
AbstractLet p≡1(mod4) be a prime. Let a,b∈Z with p∤a(a2+b2). In the paper we mainly determine (b+a2+...
Criteria are obtained for the quartic residue character of the fundamental unit of the real quadrati...
Let εmdenote the fundamental unit of the real quadratic field Q(Vm). It is our purpose to evaluate t...
AbstractLet K be the cubic subfield of a field of the 163rd root of unity. It is proved that the cla...
AbstractLet K be the cubic subfield of a field of the 163rd root of unity. It is proved that the cla...
Let f(x) = x3 − tx2−ux−1 ∈ Z[x]. Conditions are given on t and u which ensure that f(x) has exactly...
AbstractLet p>3 be a prime, u,v,d∈Z, gcd(u,v)=1, p∤u2−dv2 and (−3dp)=1, where (ap) is the Legendre s...
AbstractLet ∈ = (t + u(d)2/2 be a unit of Q((d)1/2), whose norm = 1. We investigate the properties o...
AbstractLet ϵ be an algebraic unit such that rank of the unit group of the order Z[ϵ] is equal to on...
Dirichlet's theorem describes the structure of the group of units of the ring of algebraic integers ...
AbstractExplicit formulas are given for the quadratic and quartic characters of units of certain qua...
AbstractCriteria are obtained for the quartic residue character of the fundamental unit of the real ...
There exists a positive density of fundamental discriminants D such that the attached fundamental un...
AbstractNecessary and sufficient conditions for representing certain classes of primes by given quad...
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